Math that matters (Part I–Missing Women)

If we want kids/adults to learn math, we might as well make it relevant. Here are a few relevant calculations (that employ nothing more than algebra) which I find very relevant to our future. Imagine these calculations being taught to an 8th grade algebra class! Here is the first installment:

Missing women

Most people are not aware that females were systematically removed from the population during the 20th Century and it is a practice that continues today. How do we know? Well, as Nobel Prize winning economist, Amartya Sen, noted back in the 1990s, if we look at sex ratios of nations, we find several that have ratios that are far from 1:1. Pakistan and China have ratios of 0.94:1 and India has a ratio of 0.93:1 (in 2016) (these numbers are pretty much the same as they were in 1990, though Pakistan has improved slightly from 0.91:1). Given that women live longer than men, nations should have sex ratios above 1–most European nations are above 1.03:1. Given these “small” differences among nations, one might just dismiss the low ratios as “normal” variation. Unfortunately, this would be a huge mistake. Here is the math to determine what a ratio of 0.93:1 means, in comparison to a 1.03:1.

First, let’s define the variables needed:
F = number of females in a population
M= number of males in a population
T = total population = F + M
R = sex ratio = F/M

So the above two equations have 4 variables (F, M, T, & R)…if you know two (and you do, T and R, from Internet sources), you should be able to use simple algebra to compute the other two, F and M.

Again, the equations are: (1) T = F + M and (2) R = F/M

Here is how you solve these two equations:
Solving (2) for M yields (3) M = F/R, substituting (3) into (1) yields, F + F/R = T; this can be rewritten as: F(1+(1/R)) = T
which can be rewritten as
(4) F = T/(1 + 1/R)

So, you can determine how many females are in a population using this equation. This can be considered the Actual Females (Fact).

So, with a population of 1 billion (1,000,000,000; which is smaller than both India’s and China’s current population) and a sex ratio of R=0.94, we use equation (4) to solve for Fact as such:

Fact = 1,000,000,000/(1 + 1/0.94) = 485 million
So, Mact = 1 billion – 485 million = 515 million

Now to determine the Expected Females (Fexp) in a “healthy” society, with F/M = 1.03, we use equation (4) again with this new R value.
Fexp = 1,000,000,000/(1 + 1/1.03)) = 507 million
So, Mexp = 493 million

Now you can determine the “missing females” (Fmiss) using this simple formula:
Missing Females = Fmiss = Expected Females – Actual Females = Fexp – Fact

In our example above (the hypothetical nation of 1 billion people), we find:

Fmiss = 507 million – 485 million = 22 million

Is this a large number? Well, when one considers that between 50-60 million people died in World War II, I’d say it is! Also, this is only for one country (say China or India). If you were to add up all the nations in the world with “missing women,” it comes to close to 100 million! Now that is an abominable figure, isn’t it? Yet, how many of you have heard of this figure before? If you are wondering why women are missing, do some research. It isn’t a pretty story. (I wrote about this issue over 10 years ago and got it published in a local paper’s front page. Sadly, as I recall, it hardly drew any attention.)

Just to put these numbers in perspective it is sometimes valuable to imagine what a sex ratio looks like when you bring it down to a scale that we can see. Let’s say, if you had a party of 100 people and a sex ratio of 0.94, you would have 52 men and 48 women. This would hardly be noticeable, would it? Hence, now we see why we need to do the large-scale calculations to expose something very sinister.

lessons learned in 2016

[Note: some of these lessons were mere reminders but even so they were still noteworthy if only that]

We don’t live in a democracy. Despite our repeated boasts about how we live in the “greatest democracy” of all-time, we must come to terms with the fact that we don’t. Evidence? While too abundant to mention exhaustively in a BLOG, here are a few of the most compelling to me: the Electoral College (ref 1), extensive voter suppression (before election day, on election day, and after election day) (ref 2a, 2b), inability to have a full recount (in several states) (ref 3a, 3b), extensive use of “no paper trail” electronic voting machines (ref 4a, 4b, 4c), exclusive “two-party” Presidential debates (ref 5a, 5b, 5c), and dominant media forms that fail to hold candidates accountable (ref 6a, 6b, 6c).

No country is above electing a racist, sexist, xenophobic, egomaniacal person. Largely because of our failures in democracy, a person with horrific human qualities was given a chance to win/steal a presidential election. According to the Democratic Party’s leadership, a Russian computer hacking or a FBI director’s questionable action had the most to do with Clinton’s loss. However, this take wrongly deflects us from the more significant reasons, many mentioned earlier; this misfocus by a major party isn’t surprising given the little attention they have paid to the other factors (factors, sadly, they seem to accept as “normal”). Add to these, significant miscalculations in strategy (including, saying that many people were “deplorables” and claiming that things are going quite well (as if neoliberalism is good), when they aren’t (and it isn’t)).

Too many continue to spend 90%+ of their political energy focused entirely on the presidential race. This is probably the most vexing to me. I see it in my own community. If only a couple of handfuls of citizens would dedicate themselves to the local political process signficant &*#$ could happen. Hopefully, now that folks see how discombobulated the national election scene is, more will look to act locally.

Misogyny is alive and well! When I first read that White women actually voted more for Drumf than HC, I was shocked (source). I didn’t believe it. When I heard some women easily discounting the blatantly misogynistic statements revealed by Drumf recordings, disregarding it as mere “boy” or “locker room” talk, I was sickened. How could this be? It is clear that the extreme attack on Hillary, one that has lasted more than a decade, has worked. She was built as the devil and enough people came to believe this. (She may not be an ideal candidate but she is no devil.) Also, this attitude is consistent with our generally condoning of violence (physically as well as economic) against women (and people of color) for hundreds of years, examples which have become more easily revealed to us by cell phone videos and texts. Clearly, we all must be more vigilant to expose and censure sexist and racist actions/statements. They are reprehensible and no person who revels in them should ever have the opportunity to be our commander-in-chief. I thought we had made more progress but recent events suggest we still have a long way to go.

Cancer is as debilitating mentally as it is physically. I’ve come toe-to-toe with this disease. It is something that many of us still don’t openly discuss (out of fear?) and yet it affects more and more of us every day. I applaud those that provide care to those who are sick. The doctors, nurses, social workers, and other care givers, often who work exhaustive hours even on holidays, deserve a lot of admiration.

Despite all the fear, hatred, irrationality, and hopelessness that we are fed every day, many good things continue to happen. Every day people are growing TONS of food in Detroit and elsewhere (ref 7), renewable energy is booming almost everywhere (such as the Philippines, ref 8), and volunteerism continues to thrive as well (ref 9). So, as we begin 2017, remember what the great Frederick Douglass said 160 years ago: “If there is no struggle, there is no progress.” (full speech here: ref 10).

Grandpas on Memorial Day

Memorial Day is a great day to reflect on history. Whether it was started by former slaves in Charleston, SC honoring a mass grave of Union soldiers in 1865 (ref 1, ref 2) or Southerners in other cities (ref 3) celebrating the sacrifices of loss Civil War soldiers a year later, we now have a tradition deeply embedded in our culture. Going back to the founding of the US, well over 1 million U.S. servicemen and servicewomen have died fighting wars. And, not to be overlooked, millions of others, many from foreign lands, have died or have sustained significant injuries, physical and mental, as a result of these conflicts.

Both my grandfathers fought in the “Great” wars of the 20th Century, Joseph (in WW I) and Max (in WW II). While Grandpa Joseph sadly passed when I was just a toddler, Grandpa Max and I got to spend ~30 years getting to know each other. Grandpa Max taught me many things, but probably the two most important were: (a) everyone matters and is worth your attention; and, (b) when something is important enough, you must be willing to sacrifice everything to obtain it (in 1945 that was freedom from fascism; he volunteered to serve, and, as a result, fought in France against the Nazis). Despite risking so much and contributing to the “Victory,” Grandpa Max was no fan of war. He openly protested against all other U.S. wars, which he thought were illegitimate on moral grounds (he deemed them imperialistic enterprises). He was a working man, whether it be in the Bowery of New York City, as a diamond setter, or a social worker with schizophrenics later in life. He never made much money but he quietly saved thousands, which he generously gave his five grandchildren at his passing. He was modest and definitely a bit cantankerous (what older men aren’t). I don’t know for sure, but I think his battlefield experiences connected him with humanity in a way few of us ever do. His two sons drew from these lessons as well–both have dedicated their lives to the betterment of humanity.

We definitely have a lot to learn from our soldiers and the experiences they have had; I wish I had had more opportunities to learn from Grandpa Joseph. But given that face-to-face combat is becoming less common (at least among U.S. soldiers) as drones and airstrikes become more popular (both further dehumanizing combat), we must be vigilant not to let war become something that we participate in casually or without exhausting all diplomatic options first. I am sure Grandpa Max and Grandpa Joseph would agree with this.